Problem Solving

QUESTION STEM:
For all positive integers m, m=3m when m is odd, and m=1/2m when m is even.
Which of the following is equivalent to 9x6?
A 81
B 54
C 36
D 27
E 18

Personal solution: I plugged the even and odd numbers in the relative formulas, and came up with 81.
To my surprise, the correct answer is 27. Can anyone help me understand why?

Thanks to everyone who will help!

Giovanni[/img]

The problem has been transcribed incorrectly.
In the original problem, all of the answer choices including function notation.
The following represents the intent of the problem:

For all positive integers m, @m=3m when m is odd and @m=(1/2)m when m is even. Which of the following is equivalent to @9 x @6?

A - @81
B - @59
C - @36
D - @27
E - @18

Since @m=3m when m is odd, @9 = 3*9 = 27.

Since @m=(1/2)m when m is even, @6 = (1/2)6 = 3.

Thus, @9 * @6 = 27*3 = 81.

Notice the @ symbol in the answer choices.
The correct answer must be the EQUIVALENT of 81.

Answer choice D: @27
Since @m=3m when m is odd, @27 = 3*27 = 81.

The correct answer is D.

Answer choice A is A TRAP.
Always beware of an answer choice that seems TOO EASY or TOO OBVIOUS.

GATGuruNY - spot on my mistake.
I overlooked the symbols.
Thanks for your clarity!

Giovanni

GMATGuruNY wrote:The problem has been transcribed incorrectly.
In the original problem, all of the answer choices including function notation.
The following represents the intent of the problem:

For all positive integers m, @m=3m when m is odd and @m=(1/2)m when m is even. Which of the following is equivalent to @9 x @6?

A - @81
B - @59
C - @36
D - @27
E - @18

Since @m=3m when m is odd, @9 = 3*9 = 27.

Since @m=(1/2)m when m is even, @6 = (1/2)6 = 3.

Thus, @9 * @6 = 27*3 = 81.

Notice the @ symbol in the answer choices.
The correct answer must be the EQUIVALENT of 81.

Answer choice D: @27
Since @m=3m when m is odd, @27 = 3*27 = 81.

The correct answer is D.

Answer choice A is A TRAP.
Always beware of an answer choice that seems TOO EASY or TOO OBVIOUS.